Solve (3x + 2y) ^ 2 - (x - y) ^ 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(3x+2y)^{2}-(x-y)^{2}$$

Evaluate

$\left(4x+y\right)\left(2x+3y\right)$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(3x+2y\right)^{2}$.

$$9x^{2}+12xy+4y^{2}-\left(x-y\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-y\right)^{2}$.

$$9x^{2}+12xy+4y^{2}-\left(x^{2}-2xy+y^{2}\right)$$

To find the opposite of $x^{2}-2xy+y^{2}$, find the opposite of each term.

$$9x^{2}+12xy+4y^{2}-x^{2}+2xy-y^{2}$$

Combine $9x^{2}$ and $-x^{2}$ to get $8x^{2}$.

$$8x^{2}+12xy+4y^{2}+2xy-y^{2}$$

Combine $12xy$ and $2xy$ to get $14xy$.

$$8x^{2}+14xy+4y^{2}-y^{2}$$

Combine $4y^{2}$ and $-y^{2}$ to get $3y^{2}$.

$$8x^{2}+14xy+3y^{2}$$

Expand

$8x^{2}+14xy+3y^{2}$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(3x+2y\right)^{2}$.

$$9x^{2}+12xy+4y^{2}-\left(x-y\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-y\right)^{2}$.

$$9x^{2}+12xy+4y^{2}-\left(x^{2}-2xy+y^{2}\right)$$

To find the opposite of $x^{2}-2xy+y^{2}$, find the opposite of each term.

$$9x^{2}+12xy+4y^{2}-x^{2}+2xy-y^{2}$$

Combine $9x^{2}$ and $-x^{2}$ to get $8x^{2}$.

$$8x^{2}+12xy+4y^{2}+2xy-y^{2}$$

Combine $12xy$ and $2xy$ to get $14xy$.

$$8x^{2}+14xy+4y^{2}-y^{2}$$

Combine $4y^{2}$ and $-y^{2}$ to get $3y^{2}$.

$$8x^{2}+14xy+3y^{2}$$